Its true, anti-parallel Schottky diodes will get lower even harmonics, but this is valid only if at the input is an ideal sinusoidal signal (fundamental only, free of harmonics).
If there are already even harmonics at the pair diodes input, even harmonics will have consistent amplitude at the output (as in our case where the MMIC is in saturated region, due to high LO input).
I would recommend to try the circuit using only one diode, and see the difference in levels (in this case don't forget to place a resistor in parallel with the remaining diode, for current return).